The process that historically forces the do, re, mi
scale into existence is not hard to grasp.

When a note is played, on a flute or by any instrument,
the note is determined by how many vibrations per second it makes. Concert
"A" for the orchestra is 44o vibes per second, for example.

If you play or sing the octave to any note (the
"same note, only higher"), then it has twice the vibes. The ratio
between the notes, then, is 2 to 1 (or 2:1). That's
all you need to know that invloves any numbers.

Historically, the ear has preferred simple ratios as
harmonious, and complex ratios have been avoided or considered noisy or
dissonant (to be used only as an artistic contrast to harmoniousness --
as a sort of 'dueling tonalities').

For example, two notes on the piano right next to each
other have a complex ratio (play them together to hear this) and these
kind of ratios cause "beats" -- a kind of repetitive "wow-wow-"
effect, which is physically measured as unpleasant to the ear.

You also need to know that whenever a single note, like
"A," is played, we actually hear several notes at once, called
overtones. They're very faint, but the different strengths of the
mixture is mainly what tells us we are hearing a trumpet instead of a piano
or a voice -- but all sounding what seems like the same single 'A'
note.

Now here are the grabbers:

* The most audible overtones
of any one note add up to its major chord, when played out loud
rather than as overtones: Tonic, Fifth & Third.

* The most audible overtones
of a tonic or keynote all have simple ratios, like 2:1 (octave), or 3:2
(fifth note of scale), and the 4th note of the scale, whose first different
overtone is the given tonic, has a ratio of 4:3 . In fact these three notes
are present in virtually every musical scaleknown on earth.

* If you write out the overtones
of these three notes and string out the three most audible ones of each
within the span of an octave, you will get the major scale:

Tonic C: Overtones
are: C, G, E, and Bb (I've
left out the additional octave overtones as redundant and too high and
weak to be noticed within the framework of average human hearing.)

Fifth G: Overtones
are G, D, B, and F

Fourth F: Overtones
are F, C, A, and Eb.

* If you substitute the
three weakest ones (the 3rd, 6th and 7th notes of the scale) with another
three notes (which includes the even weaker next overtones), and which
are flatter, you get the minor scale. (The 6th note is strongest
of the three because it forms no complex ratios with adjacent notes in
the scale.).

* If you leave these two
-- the 3rd and 7th notes -- out altogether, you get what's called the
'Chinese scale' -- or the piano 'black notes' pentatonic 5-note
scale -- found also in Africa, old Scottish and Irish folk music, and elsewhere.

* Because these overtones
are very weak, they were the last to come into the scale, and how to tune
them was a matter of historic uncertainty -- and many people tuned them
somewhere between minor and major (in the 'cracks' on the piano), producing
what are known as 'blue' or neutral notes. (For
more detail on this historic [and prehistoric] process of how the overtones
slowly pressed their way into human scales and awareness, creating so many
similar 5 and 7 note scales in times and cultures with no contact, click
here.)

* When you further consider
the advent of harmony (in which there has been
use of only the three chords of the tonic, dominant(5th) and subdominant
(4th)) to harmonize all the 7 scale-notes in most of
the folk melodies known, this further underscores that these three notes
and their overtones were fundamental influences in the formation of the
scale's notes. Even the names that evolved for them are perfect representations
of their acoustic role, even though the names ('dominant' 'sub-dominant'
& keynote/tonic) were also coined by people without acoustical knowledge.

Now either all this is the greatest coincidence
on earth-- that is, people who knew nothing of acoustics coming
up with scales reflecting all these acoustic properties purely
by chance -- or else, in fact, the ear was already able to discern
the sounds as distinct between harmonious or dissonant because the ear
could hear these acoustic properties without consciously knowing they existed.
I have chosen to believe the latter, and in 1970 wrote The
Origin of Musicin order to demonstrate this idea more fully.
Since that time there is confirming evidence in the 'babies experiment'
(Trehub & Co.); the Kilmer et al, oldest song being in harmony
and using the diatonic; and the oldest known instrument (Neanderthal flute).

The glaring question in all this is the apparent absence
of the full diatonic scale in so much of Asia and elsewhere. While the
diatonic is found in much of the world, including Africa
(Tracey; see also Nettl) and the near East, the Pentatonic
scale predominates as well, or even exclusively, in a huge part of the
non-European world (along with many other non-pentatonic nor diatonic scales).
People raised on the music built by scales like these become used to them
and the scales are entwined in the cultural matrix of the culture for many
generations.

In early music of Scotland, Ireland and the Orient one
can often find the missing 3rd and 7th notes of the scale being used not
as part of the official scale, but as passing notes or leading
tones. That is, they are notes in the gaps that 'lead' 'to the fourth
or 'pass over into' the octave. In different cultures the names for this
are different, but have similar meaning. The Pien tones in Chinese
pentatonic scales mean 'becoming' that is, a 7th 'becoming' the octave,
in a sequence of melody or scale notes. The words are different, the concept
and usage is similar. This is widely reported among musicologists and anthropologists.

But in many places, not even these leading tones can
be found. Sometimes they are used but 'banned' by tradition or religious
authority. This dichotomy -- between official or religious systems of music
and the actual practice among the common or pagan component of the population
(who far less often could keep records or had notation as often did the
heirarchical keepers of musical systems) -- is a dual history that has
been recognized by numerous writers, exisiting in various ways in Europe
as well as in the Orient and the Near East. [See Carl Engel, Music of
the Most Ancient Nations, pp. 151-3; Curt Sachs, Rise of Music in
the Ancient World pp. 116-118, 121; Fink, Origin of Music, pp
107-115, and many other sources).

But still, even when we consider this, the pentatonic
and many other scales still can be found in places with little or no reference
to anything like the diatonic.

Unfortunately, our life-spans and personal experience
(especially in the recent past and earlier) rarely embraced enough time
to see all aspects of the evolutionary world in motion. In a real sense,
our experience is like a still-photo of a bird in flight. The bird (in
the photo) could lead to the conclusion (based only on that one frame)
that it is 'still,' but in reality, it flies. Taking evolutionary reality
in general, we usually don't live long enough to see the next frame of
it nor the previous frame -- except when histories give us a clue (in so
far as they are accurate).

But if we use our best efforts to fill in the frames,
based on our research into the past, then we can rise above the 'still-life
picture' limits of our personal experience and immediate surroundings --
and dimly see the forest, not just a few trees; see the whole,
not just the part; see the motion, not just the fixed bird.

Specifically, we don't consider the pentatonic scale
as a contradiction to the acoustic, nearly-subliminal pressures that bring
the diatonic scale into existence over long periods of time and across
cultures, but instead, we see it as an earlier, or different but equal
version, of the same acoustic influences and process.

AFRICA -- DIATONIC

From: Andrew Tracey,

International Library of African Music,

Rhodes University,

Grahamstown 6140, South Africa.

...Very little evidence from Africa is adduced,
but what it could add would be support for the existence of diatonic type
of scales in certain regions, of scales clearly based on the harmonic series
in others, and of equal-spaced scales in yet others.

As regards the number of notes in the octave,
according to Hugh Tracey's measurements of numerous instruments during
his 40 years of research in central, eastern and southern Africa, approx
40% of Africans use pentatonic scales, 40% heptatonic, and the remainder
either hexa- or tetratonic scales. A look through the catalogue of
our Sound of Africa series of recordings, 210 records recorded by Hugh
Tracey, would give you a good deal of evidence of actual African tunings,
recorded in Hz. [Emph. added]

Yours,

Andrew Tracey, ILAM

E-mail: ilat@giraffe.ru.ac.za
Webpage: http://ilam.ru.ac.za

"The hallmark
of great science is that it reduces complexity into simplicity"

An imperfect analogy to the process
of the evolution of the scale can be seen in this illustration.

Above, the grooves and the force of gravity represent
the influence of the overtone series and the laws of acoustics upon the
human ear - the "ruts & grooves of nature," so to speak.
The balls in the illustration represent the free motion and random production
of all sounds and musical tones made by the voices and instruments of all
musical cultures through historic time, including dissonance as well as
consonance.

There have been a huge variety of complex and simple
sounds, including half-tones, quarter-tones, partial tones and many scales
produced. However, the greater the passage of time, the greater
the number of tones or balls will fit and fall into the musical scales
dictated by the influence of nature's "acoustical" grooves (and
this happens because many of the louder overtones of a note are subliminally
audible & consonant).

The balls pictured larger above cannot fall or fit into
the grooves. They represent tones that have "grown large" with
attachments or social associations, such as sounds, tones and instruments
that last through limited time periods without much evolution because they
are fixed by ritual -- such as religious chants, or fixed by other traditions,
such as "blue notes" in jazz, or seasonal or holy-day celebration
music, or other non-acoustical tones.

If these tones have no other viability outside their
cultural or social attachments, if they had no previous or additional match
to the grooves (i.e., no acoustical basis), then they can disappear when
the institution, ritual or tradition to which they were fixed also fades
into history or fades from historical musical significance due to social
change. Thus a process of evolutionary selection takes place in which the
cultural influences may change, but the constant, cumulative and
least variable influence is that of acoustics.

However, the process is never "purely"
acoustic nor cultural, because in all social change, new cultural effects
will replace old esthetics as long as humans develop cultural paradigms.
-- Bob Fink

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Additional note on
the Evolutionary Process

-

One fundamental idea that should
have been given more prevalence in these webpages is that general human
evolution has provided us with voices that are acoustically musical, and
with ear receptors that are appreciative of, or attracted to, acoustically-musical
sounds (i.e., not noisy).

Without these physiological capacities,
then:

* Mothers would not coo to their
babies; nor would the babies love it;

* Nor would evolution of language
and the socializing sounds of the voice have been as possible;

* Nor would the noisy (i.e., non-acoustically
musical) sounds from any nearby destructive event or attack, or of the
sounds of breakage, screams or cries of pain, have served as a noisy warning
[unattractive or repelling] to alarm or alert us -- Some sounds make us
come, others make us run....

And, as a result, our collectivized
survival might not have been as efficient, and we could have gone
the way of the extinct Dodo.

All those same capacities [regarding
distinguishing noise from "musical" sound] also served to allow
the development of musical systems to arise and evolve wherever there were
curious people with time to play or experiment with the stimuli around
them.

Scales Come From
Melodies

It's my belief that melodies first existed vocally, and
then instruments, like flutes, were made to produce the most commonly used
notes in a favoured melody or melodies. This would produce, in effect,
a general "scale" on an instrument [even before a concept of
"scale" existed], but it wouldn't necessarily play all other
favoured melodies containing intervals sung differently.

As a result, many flutes would be needed with slightly
different intervals -- which we still have in modern times, by using valves,
or making flutes with different keys. [In the case of the piano, we temper
the whole twelve notes and scale, rather than making different pianos tuned
for playing in different keys.]

While many flutes have unequally spaced holes,
which usually produce perfect acoustic intervals, the common equally-spaced-holes
flutes were made -- not only to suit the convenience of finger-width and
spread -- but likely also as a rudimentary attempt at "temperament"
-- allowing all melodies to be played almost in tune, all holes being just
slightly "off-key" or containing non-acoustic or complex-ratio
intervals.

Musicology and ethnomusicology observers over the years
have repeatedly reported that singers in various cultures and times
would rarely match the tempered flutes that accompanied their singing,
preferring to sing perfect acoustic intervals despite the instrument. This
shows that a concept of "in tune" existed vocally.

These complications alone have made evolution of the
scale a rickety path.

PROOF THAT CULTURAL CONDITIONING CANNOT EXPLAIN REACTIONS
TO HARMONY, DISSONANCE AND PERCEPTIONS OF UNISON IN MUSIC.

Debunking the "Getting
Used To It" Theory

(Excerpt from The Origin of Music, by Bob Fink)

As this idea, that we like what we like because we are used to it,
has been often mentioned in this chapter, and as I have mostly avoided
confronting it directly throughout the book, I would like to take it up
here now in detail.

There has been a hesitation about relying upon one's own ears to judge
whether music has a "natural" foundation or not.

People are wont to say about Western music, "I grew up with this
music, I'm used to it, and so naturally it sounds right to me. My judgment
would be altogether useless in trying to determine such a thing."
I can't help but to mostly agree with such people, who are products of
this society and whose tastes are products of growing up with Western music.
Even if there were nothing "natural" about Western music, they
might still like it.

But with a little digging and careful analysis, the fact that there
are things natural about music can be demonstrated even to our Western
ears, things which cannot be explained by our ears having been trained
or conditioned, or by our having "gotten used to" certain relations
of tones in Western music.

1. If I play a G and the F next to it, on any instruments, or even
on tuning forks without overtones, no one can mistake that there are
two notes (or more, if we are "untrained") being played.

But if I play an octave on a piano which is well tuned, only
a semi-trained ear, used to hearing these sounds, can always tell
that I am playing two notes, and not only one. Many will think it
is one note being played.

And if I hit two tuning forks which make this octave, no one
can tell that I'm playing two notes. They will sound like only one note!
In fact, if I hit four notes on tuning forks, C, G, E and Bb, all in the
range and intensity in which they would appear as overtones of C on the
piano, not a soul can tell that I'm playing more than one note. It would
sound like one, lone C sounds on the piano.

Now how are the reactions described here in the above three paragraphs
to be explained by our ears being a product of Western music?

2. Better still, if I play a G and F together, most people, who are
not out to "get" me and my theory, will admit they sound relatively
dissonant. (You might like this sound or not; but whether you do or not,
you will have to admit the two notes sound very different from
each other.) Fig. 1:

But if I play the same two notes, G and F, and add to them a
B and D and an octave of Gs in the bass, then they sound, not dissonant,
but very harmonious: (Fig. 2):

The above chord includes the F and the G, and in addition, an octave,
G-G, and other intervals about which I expect to be told: "We are
used to hearing the combinations in the context of that chord, so it sounds
better to us in that context and worse in isolation."

OK, Let's grant that. G and F sound good in context and bad in isolation.
(Note: G and F are played together and sound consonant as the beginning
of that old saw "Chopsticks.")

But, continuing with this, suppose I play the octave, and the
G and F, which is in the above chord, "in context?" - That is,
in the above chord? And THEN, suppose I play them out of context,
each by itself?

If both, this octave, and the other harmony of G and F, were consonant
because we are used to hearing them in the context of the above chord,
that is, because this context is responsible for our "expecting"
them and thus sounding good to us - then
why do not both intervals, G plus F, and the octave G-G, sound dissonant
out of context? Why does only the G and F
harmony sound dissonant out of context? Why does only
the octave sound consonant out
of context as well as in this
context?

Indeed, taking the above chord itself, we can ask, why does the whole
chord sound consonant outside the context of a musical work, while other
chords do not? If all chords, according to a "getting used to"
theory, are innately as consonant as any other chords, that is, all capable
of being considered consonant or dissonant at society's dictation, making
us "used to" some chords and not others, then why aren't all
the chords we are thus used to also consonant sounding to us when they
are played by themselves? Why aren't they as consonant sounding as
they seem to be when so beautifully placed in the familiar context of a
musical work? Or why isn't every one of them dissonant sounding to us when
they are played by themselves out of the musical context which presumably
is responsible for our having gotten used to them? Why are some of
these chords always consonant, in and out of context, and others
consonant only in context, if we are "used to" all of them?

To hear an excellent
example of this, click here, and for another,
clickhere.

Our very own perceptions of things do not conform to culturalists'
suppositions about how we got those perceptions. Instead, they prove
that we cannot be totally conditioned to perceive harmony or dissonance
or, certainly, unison. The conditioning theory of consonance
and dissonance is simply not a total explanation, and likely not even a
good one either.

-- Bob Fink

Copies of The
Origin of Music -- An Essay, are available from: GREENWICH
Publishers: 1829 Arlington Avenue, Saskatoon Saskatchewan, Canada, S7H 2Y9
for $20.oo (U.S.) +shipping

I'll put my chart of overtones (picking the key
of C arbitrarily) right here to refer to as I answer your letter: [The
parallels of this simple chart to the evolution of scales is astounding.]

Note or 1st

overtone

1st DIFFERENT overtone

2nd different overtone

3rd different overtone

Tonic: C

G

E

Bb

Dominant/Fifth: G

D

B

F

Subdominant/Fourth: F

C

A

Eb

Now here are some known historic operating principles
capable of being considered universal or nearly so:

*The
"tonic" (for lack of a better term), and its fourth and fifth,
are almost everywhere used in scales, and their overtones are most frequently
heard, although were not necessarily heard consciously as different notes.

*In the course of making scales, Helmholtz
has noted, I believe accurately, that most peoples have avoided notes
in their scale which produce semitonesas melodically dissonant.Semitones are admitted only apparently
when justified by being melodic "leading tones" [whether
moving melodically upward or downward] to one of the strongest notes (tonic,
dominant or subdominant).

*The overtones of a note, as listed above,
become (generally) weaker or less audible from left to right (which
answers, as you asked, "Why do you say [taking only the first 3 of
the 4 columns in the chart] that the third and seventh tones {E & B}
are the weakest overtones?")

*The octave to a note is usually considered
or treated as "the SAME note, only higher."

------------------------------------------------------------

Now we can put all this together -- the chart
plus using the operating principles to interpret the chart.

You wrote: "If I understand correctly,
you say that the major scale is the sum total of the first four overtones
of the dominant, sub-dominant, and dominant."

Actually, using only the first two DIFFERENT
overtones in the chart above (plus the original fourth, fifth and tonic)
these produce (when placed within an octave) the series of notes we call
the major diatonic scale: C, D, E, F, G, A, B, C(Octave)

However, since the overtones known as E, A and
B are not much more audible than the ones known as Eb and Bb (the 4th ones
in the chart above), then it's reasonable to assume that awareness of them
as exact pitches might be a subject of confusion or debate when it came
to choosing which (the 3rd or the 4th overtones) were felt
should go into the scale. [This is borne out in history by these notes
being variously or widely tuned at
various times and places.] -- Or -- They could be left out
altogether.

If scale-makers choose ALL the 3rd and 4th overtone-inspired
notes, B [and Bb], E [and Eb], then the resulting
scale has too many semitones to be tolerated, which is historically proven,
as few or no such scales exist anywhere. (C, D, E, Eb, F, G, A, Bb, B,
C)

You wrote: "...you say that the third
and seventh tones of the scale are the weakest overtones and are therefore
sometimes left out, thereby resulting in the pentatonic scale."

Yes -- If none of these 2nd and
3rd overtones are chosen (neither the E nor the Eb, and neither the B nor
the Bb) then we see the pentatonic scale. The A alone remains acceptable
when either the major-scale or no choice is made, as it produces
no semitones to the other scale-notes in either the diatonic or
the pentatonic. (Pentatonic: C, D, F, G, A, C)

If scale-makers chose the Eb and the Bb to REPLACE
the E and B, then you are close to the minor scale. However, we now have
a semitone from the A to the Bb. If we flatten the A to Ab, we have the
minor scale, and now the Ab-to-G semitone perhaps was acceptable
or seen as a "downward leading tone" to the 5th. [Note:
The Ancient Greeks conceived their scales or "modes" downward
(as may have other cultures in the past), and their favourite was not
the scales like our major or minor, but was the Dorian, which
has such downward leading tones (such as the minor-second or minor "re")
to the tonic. -- See additional interesting note
below on this topic.]

This chart is invented by me to show the great
parallel to the overall evolution of the scale worldwide,
although no human-made history is ever free of many temporal contradictions,
complications and exceptions, based on social influences and culture. But
over-all, this chart's parallels to history is something that cannot or
should not be ignored by musicologists and composers. It cannot be
coincidence when the past scale-makers knew nothing of acoustics.

Your other questions:

"In the key of C, isn't F the first overtone
for F, and isn't B the second overtone for G?"

From the chart above you are right about the
F(as octave) being the actual first overtone of F. But the
C is the first different overtone.

Likewise, B is the 2nd different overtone
for G. (D is the 1st different one, but G is the first actual
overtone of G).

The actual series of overtones looks like
this in acoustic theory: G: Overtones: G-D-G'-B'-D'-F' (The apostrophe
means "one octave higher" than the previous listed note). In
my chart, I left out the extra repeated overtones (G' and D') for simplicity.

ADDITIONAL
NOTE ON GREEK MODES

Interesting to me is that the popular scale among
Greeks was not the Lydian (like our major) but was the Dorian (e' down
to e) -- and here's possibly why:

In downward playing, the semitone-jumps of the
Dorian are IDENTICAL to the semitone-jumps when we play our major scale
upward:

When Glareanus [16th century] measured usage
of the medieval modes, he claimed the Ionian and Aeolian were most frequent,
which are like our major/minor scales. It's interesting that, after the
Greeks, when the modes came to be played upward, the popularity
of the arrangement of semitone-jumps is what persisted (e.g.,
Downward Dorian in ancient Greece and upward Ionian in medieval times).

That's probably because, when played according
to the semitone-jumps, there is a halftone at the end of each scale that
serves as a melodic "leading tone" to the final note (F to E
in the downward Dorian, and B to C in the upward major [or "Lydian"
in Greece; "Ionian" in Glareanus time].

I realize your thesis (which I found by accident) is not centered on
musicology, but I can explain, if you're interested, why the minor key
is "sad" -- or more accurately, why it evokes a richer or wider
range of emotions than the "bright" major key.

In brief, the 3rd note of the major scale (Mi) is the note which, if
made flatter, will essentially create the minor scale. (The 6th note should
also be flattened to avoid dissonance or to balance the minor third in
the scale.)

The major 3rd is less sad (or the minor 3rd is more sad) simply because
the major 3rd is more harmonious than the minor third, which has a more
complex ratio of vibrations. In other words (plain english), the minor
is more on the edge of discord than is the major. If you accept psychologist/musical
test conclusions, which I do, then discord or dissonance creates a sense
of physical pain in the ear -- very mild pain of course. It is avoided,
or repells the listener.

But, if the discord ALSO has the charcteristic of being nearly or "almost"
harmonious, then there is an also an attraction as well as a repulsion-like
physical response, into which many compex or stressful emotions can be
read by the listener.

Harmony without the fetters of much, or any discord at all, is like
contentment -- it has an "everything fits nicely" feeling; no
loose ends, little or no ambiguity. These "happy" emotions are
also simpler (like driving on a smooth road) or are more physically integrated
in our bodies than stressful or "sad" ones (like driving on a
rough surface). It is basically a matching of emotional roughness to the
degree of roughness of the sound.

Other factors (culture, upbringing, habit, associations) play a big
role, but the acoustic explanation seems most illuminating of all.

[NOTE: If a fast bouncy
rhythm is coupled with the minor key, any feeling of "sadness"
would be greatly lessened or eliminated. If the rhythm is slow, it would
often be enhanced. This might be true for other cultures as well, because
of the physiological aspects of rhythm & discord being common to all
humans, although as mentioned, these reactions might be modified by cultural
conditioning.]

"I have lived in Central Africa for over twenty years, but to
my knowledge I have never heard an African sing the 3rd and 7th degrees
of a major scale in tune." Merriam notes (pp. 71-72): "There
has been some discussion of an African scale in which the third and seventh
degrees are flatted or, more specifically, neutral between a major and
minor interval. This concept has been advanced especially by those concerned
with analysis of jazz music, since in jazz usage, these two degrees of
the scale -- called ‘blue' notes -- are commonly flatted and since the
third degree, especially, is frequently given a variety of pitches in any
single jazz performance.

Helmholtz [Hermann C. F. Helmholtz, On the Sensations of Tone 2nd English
Ed.; New York: Dover Publications, Inc., 1954, p.255] notes that the "history
of musical systems shows that there was much and long hesitation as to
the tuning of the Thirds...."

[Add'l notes on effects of sound:
CONTINUOUS SOUND]

Almost all of us know from our own experience how the sound of a fan
in a room, or the sound of an air-conditioner, can be masked out or relegated
by our minds to a "background" noise that we no longer pay attention
to, and we get on with conversations, or watching TV, or reading, etc.
We also do this with the sound level of background converstion in a restaurant,
or the hiss of a tape when listening to a tape of music, or the sound of
our car motor while listening to the radio and concentrating on driving.
We push it out of consciousness, although we still hear it subconsciously
and it's always there. When the sound shuts off, then most of us become
consciously aware of it again , and often say something like: "Whew,
what a relief -- I had forgotten that noise was there till it stopped."

This is what makes noise pollution so insidious in its harmfulness:
We often push it into the background, and we can function, but it still
will be placing stress on our systems. Too much of it can alter our moods,
and shorten tempers, and the like, and many of us living with constant
urban noise never know the reasons why moods are not what they used to
be. The UN health organization has named noise pollution as now one of
the world's major health hazards.

DISCONTINUOUS (INTERRUPTIVE) SOUND

Our ability to push noise into the background becomes impossible for
most of us when the noise is not continuous. Even very soft sounds can
be tortuous, like the drip, drip of a leaky faucet. It's the contrast between
the noise and the silence between the noises that causes it to be interruptive
and our system cannot comfortably keep adjusting to the sudden change.

For example, we can adapt to the colour of sunglasses, and then ignore
that hue -- but if a light or lightbulb is flickering from one hue to another,
then we cannot read, or even stay in that place, as we cannot ignore or
"mask" this stimulus into the background. The same is true in
the difference we'd notice when someone puts their hand around our shoulder,
which may be tolerable for a time, but that same person would severely
annoy us if they spent that same time poking or tapping us with their finger
into our shoulder. In this last example, it isn't even loudness or sound
at all that needs to be made. Someone wiggling a finger just to the side
of your vision, while you're trying to read or even think, makes no sound,
nor touches you -- but you cannot concentrate for long, and you cannot
mask it into the ignorable background, because it doesn't have a "level"
that you can define and then mask away.

Again, the same is true with motors that have a wow-wow component to
their noise rather than being continuous, and this is the same with barking
dog's sounds. Even a dog that is barking "continuously" is really
producing a drip, drip, type of non-continuous interruptive irritant, because
no matter how small the gap of silence between barks, we can hear it, and
our physiological system cannot keep adjusting back and forth, from the
sound to the silence, in order to define its level and then mask it. The
longer it goes on, the greater the irritant, until it becomes tortuous.
Loudness has a little, but not much, to do with it. The irritant is there
as long as you can hear it.

RELATION OF THIS TO MUSIC

The continuity or continuousness of notes in a melody is created because
the previous notes often have overtones or harmonies that will usually
(not always) match the next note or notes in a fairly audible way. Thus
we are hearing "more of the same" (or at least partially more
of the same) in the succeeding notes, and this ties notes together into
a melody or continuum of sounds and/or harmonies.

This is also what creates a sense of "key" or tonality in
music and melody.

A-tonal music does not have this property of successive overtone relationships,
but in fact deliberately defies this, thus creating a discontinuous series
of tones, a-melodic, a-tonal and even a-rhytnmic. The result, based upon
the information above about discontinuous sounds, produces an irritant,
which only acculturated habit or conditioning can overcome in order for
one to aquire a sense of appreciation for it. Most of us do not, or can
not, do this.

-- Bob Fink, July, 1999

Reply from Laura:

I can't recall if I've replied to your message before, but if I have,
please forgive the duplication. Your response was just what my thesis needed!
I've taken the liberty of quoting you, almost in full. Please let me know
if you're amenable to that! Your explanation was quite lucid and very helpful
... and I fancy Bloom (the protagonist of Ulysses) would have found it
highly interesting.

Thanks very much for giving me the reason why ... it may help substantially
when I defend my thesis.

Laura

TEMPERAMENT

[NOTE The following correspondence illustrates
the nature of "temperament" and some of its significance in the
debate of whether there are any strongly influential natural bases for
scale tones and consonant intervals in the music of various cultures. --
August 1999]

Your question: "What
about the Key of "Cb" or B#?"

Dear Alice

The book "Origin of Music" doesn't
go into the issues you are interested in. But I can explain them here in
this letter. [You may have to look up the term "overtone" in
a dictionary. Basically, every note we think is a "single" note
actually produces overtones, which can be heard, but not as different notes,
but as a change in quality -- for example, allowing us to tell the difference
between a piano and a trumpet even though each plays the same note. This
is mostly due to the different strengths of the overtones of that note
in the instrument.]

A "natural 5th" is based on the first
different overtone of any given note. For example, C's first different
overtone is G, which when lowered one octave, is the natural "5th"
of C. You can produce a series of such 5ths, or a "cycle of 5ths"
as it has been called in music, such as C to G, then D (based on the preceding
G), then A, based on the preceding D, etc. Such a series or cycle looks
like this:

C-g-d-a-e, etc.

Simply put, starting on C, if you produce this
series of perfect (natural) 5ths, eventually you come round again to the
original note, but in the form of B#, which is an "enharmonic"
name for C, the original starting note. But this later C (or B#) differs
from the original C by an amount called a "Pythagorean comma."

It's a natural "flaw" -- like the days
of the year not fitting equally into one earth revolution round the sun,
with a 1/4 day interval left over. You might call that a "Calendar
Comma."

While we cannot practically shorten each day
by a tiny amount to make them fit the year by a whole number (365, instead
of 365.25), in music we CAN correct by re-tuning the notes slightly off
"natural." The way this is done on fixed-key instruments (like
the harpsichord or piano) is to divide the octave into 12 equal semitones
or half-tones.

This process is called "Temperament,"
and as a result, the notes are no longer perfect or "natural"
in relation to others. C to G is no longer a natural or perfect 5th, but
very slightly out of tune. Also as a result, B# and Cb no longer appear
to exist as separate notes in this tempered system. So you won't find music
written in these "keys," as the enharmonic version of them (B
instead of Cb, E instead of Fb, etc) is used.

As a result, in several instances, two notes
become one note (for ex, a Db becomes the same as C#, or a B# becomes a
C, or a Cb becomes a B. "Naturally" speaking, each of these examples
really are TWO different notes -- which are playable as different notes
on violin fingerings or as sung by singers).

Clearly, however, putting so many enharmonic
notes into a fixed-key instrument like a piano (putting B# as well as C,
or Cb as well as B, for example) would produce an unplayable cumbersome
instrument.

The motivation for tempering notes comes also
from transposing music. It used to be that on fixed-key instruments that
if you tuned the scale of C to perfect steps, then the scale, while sounding
perfect in C, when transposed to other keys, would sound seriously out
of tune because of the Pythagorean "error," or natural flaw.
These other keys, for example, those requiring a Db, and NOT a C#, would
be the cause of the mistuned sound. But when the 12 tones are tempered
or equalized by dividing the "error" equally among all the 12
notes, then ALL the keys are equally "out of tune" by a very
small amount, none of them so badly as to sound like a serious mistuning
to most or average ears. [However, many singers still sing the true intervals
despite what a piano plays as accompaniment. Indeed, some singers hate
the piano because they find its temperament annoying to their sense of
pitch.]

FURTHER SOURCES:

As mathematics buff Harvey Reid (in a 1995 webpage)
wrote: "Our ears actually prefer the Pythagorean intervals, and part
of learning to be a musician is learning to accept the slightly sour tuning
of well-tempered music. Tests that have been done on singers and players
of instruments that can vary the pitch (such as violin and flute) show
that the players and singers tend to sing the Pythagorean or sweeter notes
whenever they can. More primitive ethnic musics from around the world generally
do not use the well-tempered scale, and musicians run into intonation problems
trying to play even Blues and Celtic music on modern instruments."
(Not all ethnic music avoids equally-spaced notes -- especially when trying
to suit convenience of the fingerholes on flutes, which are often spaced
equidistantly, creating a "tempered" effect. See Sachs quote
below)

Ethnomusicologist Victor Grauer, in a march 3
letter to me, notes the same thing: "While tuning systems and scales
were not investigated per se in Cantometrics, it did become apparent as
we analyzed music from so many different types of society, that tunings
based on more or less 'perfect' fourths, fifths, unisons and octaves could
be found 'everywhere.' "And this came as something of a surprise,
at least to me. While, indeed, there are certain primarily instrumental
tunings which have anharmonic aspects (e.g., those based on equidistant
intervals, as already mentioned), the vocal music which was the primary
object of our study was with few exceptions something that could be notated
(roughly to be sure) in terms of the usual scales."

Notes in the Neanderthal Flute essay indicate
similar penomena:

Curt Sachs ["The Rise of Music in the Ancient
World, East & West" N.Y.: W. W. Norton & Co., 1943] and Bruno
Nettl, "Music in Primitive Culture" (Cambridge: Harvard University
Press, 1956) and Marius Schneider, "Primitive Music," in "Ancient
& Oriental Music," ed. By Egon Wellesz, Vol. I of The New Oxford
History of Music London: Oxford University Press, 1957] all write of this
general issue, each writing about a different culture::

On p. 133, Sachs describes a phenomenon in which
conflicting tendencies (toward and away from equal divisions of the scale)
may be combined. "Singers do not pay much heed to this temperament."
He adds one aria "in almost Western intervals alternates with orchestral
ritornelli in Siamese tuning." That is, singers sang the unequal steps,
but the instruments were tuned to the tempered or equal steps.

Nettl confirms this idea. He writes: "...the
instrumental scales rarely correspond exactly with the vocal scales occurring
in the same tribe." (p. 60.)

Schneider writes (p.14-15): "When the same
song is performed simultaneously...by voices and instruments, the melody
proceeds in two different tunings. The instruments...on their own scale,
the voices in theirs..." He says we must suppose "that the vocal
tone-system has been evolved in a natural and specifically musical fashion,
whereas in the tuning of instruments...quite different principles were
applied -- such as, for example, the breadth of the thumb as the standard
for the space between flute holes," or such as when a need on the
same instrument arises to transpose melodies into higher or lower keys,
the notes are adjusted toward greater equality (tempered) so that each
key will remain tolerable, if not perfect. Thus we have developed from
this kind of typical behavior an expectation NOT to find perfect pitch
tunings on an instrument.

The operative word here, relative to criteria
for what is "acceptable" is that these instruments are tolerated,
but when perfect pitch is available (voice, strings) then musicians choose
the perfect intervals. In practical terms of instrument-making, the tolerable
amounts have been in the neighborhood of up to a Pythagorean comma

These numerous observations can be taken as a
signal they are a widespread practice, perhaps universal, and is evidence
that none of it could occur so widely if there didn't exist some innate
preference for perfect consonant intervals.

-- Bob Fink

MORE on AESTHETICS

From a music discussion list, Nov. 1999:

Cindy wrote:

"When does the sound become music and
how does it happen?

"A student learns to read the notes,
learns to make sounds, learns the correct fingerings, learns the rhythms
and dynamics -- when does it become music instead of noise coming out of
the pipe? Where does that magical feeling you get when you hear a master
play come from? How do you teach someone to find it?"

Dear Cindy:

"When does the sound become music and how
does it do it?" reminds me of when a photograph "suddenly"
develops in the darkroom developing tray. The answer to your question lies
in perception of the wholerather than a mere collection of parts.

You can understand this completely with these
examples:

Look at a newspaper photograph under magnification,
so that the dots in the photo become clear.

Two things can be noted:

First: There are no grays anymore. Only black
dots of different sizes. The smaller the dot size, the more white around
them, so that when you stand back from the magnification they (the whites
and the dots) suddenly "melt" into shades of grey.

The second thing to note is:

If you can only see a small corner of the photo,
you likely cannot tell what the thing you're looking at is. (You can also
see this in a jigsaw puzzle when you have only a few pieces put together.
"What on earth is it," you think.)

Only when you stand back from the photo, or reduce
the magnification enough, can the whole of the picture "emerge"
suddenly, as if developed in a darkroom tray. This
sudden-ness is due to one's first awareness of the whole of the picture,
where until then, all you saw were too few parts to tell.

Hence the saying, "can't see the forest
for [because of] the trees." Once you rise above the trees, then
the whole forest emerges suddenly, after gaining the right height. Gaining
"perspective," is another phrase reflecting this psychology of
perception.

The same is true of music. Randomly, two or three
notes from the scale do not a scale nor melody make. Only when arranged
properly with enough notes, can you at some sudden point recognize the
scale -- or whether it is major or minor, etc.

Taking it further, when the halting unsureness
of the player becomes smooth enough; when the volume for each note is right
relative to the note before and after; when the acceleration or ritards
are based on knowing what is to come, and so, when it does come,
the deliberate pacing of the player becomes aesthetically logical and clearly
intelligent rather than amateur -- that's when it becomes music. In the
arts, all the parts must seamlessly serve the whole, otherwise it's like
a juggler who drops an item and shatters the whole illusion, or a writer
who chooses the wrong word to place in the sentence.

Other examples are legion, like the "wave"
created at a stadium sports event. The whole of the wave is unseeable when
you are too close to it, seeing only the people rising or sitting near
you. You need to gain perspective to see the whole of the illusion.

Making music is indeed like the illusion of a
magician, as you say; that "magic" instant when skill creates
and can exhibit a musical unity from separate sounds.

Hope this helps. Bob Fink

More on Scale Harmonizations

June 6, 1998

Dear Simon:

R. Reti quoted Alban Berg that in a few decades
from (the 20's) "Our [atonal] music will sound as natural
and simple as Mozart's sounds today."

So it was Berg who used the term "natural,"
not I.

I do use that term often, but I wish there was
a better one. Mozart really isn't natural sounding, and is an
acquired taste, when compared to simple non-harmonic chant or melody. The
simplest tone in nature is a single note (albeit, even these "single"
notes have overtones). When harmony is added, it is a major demand on the
senses to acclimate themselves to not hearing it as dissonant (again, by
comparison to non-harmony). So why did
humanity bother with harmony at all??

There are relationships of overtones between
the notes of a melody. That is the heart of the scale -- the 'first'
tonal melody -- or the 'essence' of melody. Harmony
tends to overtly reveal between the notes of a melody what is hidden (in
overtone relationships) by playing some of these overtone relationships
out loud. This -- in the hands of a harmonicist/composer
can either aid the connection between the melody notes as they unfold
through time, or even deliberately obscure those connections -- all to
esthetic effect.

In simplest form, the virtually universal tonic,
fourths and fifths, when their loudest overtones are played out within
an octave, can produce a variety of familiar scales. One is the whole tone
pentatonic (cdfgac -- no half-steps). If you want to bridge the gaps (where
the 3rd and 7th notes might fit) or if you want melodic "leading tones,"
then many cultures have added these from subliminal awareness of the next
loudest overtones -- as minor or major, or they compromised between major
and minor with 'neutral' or 'blue' notes.

When harmony evolves, its chords tend to underscore
or accompany notes in the melody (witness most folk songs from all lands)
also based on the tonic fourth or fifth,
depending which of these originally gave rise (by its overtones) to that
note in the scale: Thus, you harmonize
tonic (say C), with c major, D with G major, E with C major, F with F major,
G with G major, A with F major, B with G major and C again with C major.
(Try it on the piano with virtually any well-known pop or folk melody.)

This is the fundamental schemata for the harmonization
of almost all popular music. Chords were evolved in early medieval periods
following the advent of counterpoint, which created a host of accidental
harmonies (and dissonances-in-passing) of all sorts, a very serendipity-like
process. Eventually, with time, the most desired chords chosen or which
emerged most used from this process (without musicians having awareness
of the parallels they were making to acoustics -- an unknown science at
that time) ended up being the chords of the tonic, dominant and subdominant
(with variations for the minor key).

Dissonant chords were deliberately added as a
contrast to help the consonances more powerfully stand out, mirroring a
process found all through nature and other arts and disciplines: An esthetic
based on the universal interplay of polar opposites (very Hegelian/Marxist
by the way) namely: consonance/dissonance; male/female; up/down; left/right;
loud/soft; bright/dim; sweet/sour; high/low; major/minor; plus/minus; beginning/end;
negative/positive; fast/slow; -- the list is endless.

You're right, Simon -- "try writing music
without dissonance." Once we grow as a musical species beyond the
simple, clean 'pure' single 'natural' tones, and get to harmony, then within
that acquired 'non-natural' taste (like Mozart), we created a set
of polar opposites with which to develop a sophisticated esthetic as varied,
clever, beautiful, challenging, interesting (and so on) as any human relationship
woven between two (or more) different personalities.

A spectrum or color wheel of primary and complimentary/clashing
colours is of course not a painting or a work of art. It's a 'scale' (of
colours). The same with music. The scale is only the general idea of
melody in congealed form -- but music (even unaccompanied song)
is much more than any scale -- it is a composition playing off the
weak notes with the strong; the accidentals with the "naturals,"
and, with the use of harmony, this same process is enhanced using harmonies
and dissonances. You can't write music without dissonance -- OR without
consonance, I would add.

I'm sorry to tell you that any system that eschews
tonality (or a sense of key) will erase the interplay of weak/strong notes;
and a system that avoids consonance will erase the contrasting interplay
possible between dissonance and consonance. All that remains is dissonance,
texture and timbre (and sometimes rhythm although that is often scorned
as well).

Such systems of music will have adherents.
Even novices have to acquire a taste by trying things open-mindedly and
remaining skeptical of first impressions or initial repulsions. I was told
that if I hated blue cheese at first, I would come to love it beyond words
later. I doubted my host, thinking I'd never get used to eating rotten
mouldy cheese!! Good God!! But I couldn't afford to offend her (not good
strategy) so I ate it every time she made me a salad. Now I truly do love
blue cheese beyond words.

But the point is, the overwhelming majority of
humanity (check out the youth "Pepsi/french-fries" scene if you
doubt me) won't even try eating rotten moldy cheese. And that's
that.

The same with twelve tone music, serial music,
and Berg's prophesy. These will never take root in the popular consciousness,
and may even fade in the 21st century as an art only for the rarest among
us or disappear forever. There are limits to all things; and to all things
there is a season.

Scales have always been the bane of students studying
musical instruments.
Trying to figure out the key and the number of flats and sharps is confusing on
almost any music instrument.
There is a way to avoid scales though, get a
drum set!
Zzounds has a huge selection of
drums and drum sets for
you to choose from. They also have many other types of
music instruments such as electric guitars
and acoustic guitars.